scholarly journals NEW CLASSES OF HARMONIC FUNCTIONS DEFINED BY FRACTIONAL OPERATOR

2018 ◽  
pp. 1-12
Author(s):  
F. Müge SAKAR ◽  
Yasemin BAGCI ◽  
H. Ozlem GUNEY
Keyword(s):  
Harmonic Functions ◽  
Fractional Operator

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities

2020 ◽  
Vol 23 (3) ◽  
pp. 723-752 ◽  
Author(s):  
Alessio Fiscella ◽  
Patrizia Pucci
Keyword(s):  
Scalar Case ◽  
Fractional Operator ◽  
Nontrivial Solutions ◽  
Fractional Systems ◽  
Lack Of Compactness ◽  
Critical Nonlinearities ◽  
Kirchhoff Model

AbstractThis paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non–degenerate.

scholarly journals Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Time Delay ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fractional Operator ◽  
Caputo Fractional Derivatives ◽  
Picard Operator

AbstractThis study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

scholarly journals Linking the FK5 to the ICRF

1998 ◽  
Vol 11 (1) ◽  
pp. 313-316
Author(s):  
F. Mignard ◽  
M. Froeschile
Keyword(s):  
Reference Frame ◽  
Proper Motion ◽  
Harmonic Functions ◽  
Optical Reference ◽  
Precessional Motion ◽  
Precession Constant

Abstract The Hipparcos optical reference frame is compared to the basic FK5 in order to determine the orientation at T0 = 1991.25 and the global spin between the two frames. The components of the spin are significant and suggest a correction the IAU76 value of the precession constant and to a possible non-precessional motion of the equinox of the FK5. The regional errors are analysed with harmonic functions and found to be as large as 150 mas in position and 3 mas/yr in proper motion.

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